TY - GEN
T1 - Subexponential-time algorithms for maximum independent set and related problems on box graphs
AU - Lingas, Andrzej
AU - Wahlén, Martin
PY - 2003
Y1 - 2003
N2 - A box graph is the intersection graph of orthogonal rectangles in the plane. We consider such basic combinatorial problems on box graphs as maximum independent set, minimum vertex cover and maximum induced subgraph with polynomial-time testable hereditary property Pi. We show that they can be exactly solved in subexponential time, more precisely, in time 2(O(rootnlog n)), by applying Miller's simple cycle planar separator theorem [6] (in spite of the fact that the input box graph might be strongly non-planar). Furthermore we extend our idea to include the intersection graphs of orthogonal d-cubes of bounded aspect ratio and dimension. We present an algorithm that solves maximum independent set and the other aforementioned problems in time 2(O(d2dbn1-1/dlogn)) on, such box graphs in d-dimensions. We do this by applying a separator theorem by Smith and Wormald [7]. Finally, we show that in general graph case substantially subexponential algorithms for maximum independent set and the maximum induced subgraph with polynomial-time testable hereditary property Pi problems can yield non-trivial upper bounds on approximation factors achievable in polynomial time.
AB - A box graph is the intersection graph of orthogonal rectangles in the plane. We consider such basic combinatorial problems on box graphs as maximum independent set, minimum vertex cover and maximum induced subgraph with polynomial-time testable hereditary property Pi. We show that they can be exactly solved in subexponential time, more precisely, in time 2(O(rootnlog n)), by applying Miller's simple cycle planar separator theorem [6] (in spite of the fact that the input box graph might be strongly non-planar). Furthermore we extend our idea to include the intersection graphs of orthogonal d-cubes of bounded aspect ratio and dimension. We present an algorithm that solves maximum independent set and the other aforementioned problems in time 2(O(d2dbn1-1/dlogn)) on, such box graphs in d-dimensions. We do this by applying a separator theorem by Smith and Wormald [7]. Finally, we show that in general graph case substantially subexponential algorithms for maximum independent set and the maximum induced subgraph with polynomial-time testable hereditary property Pi problems can yield non-trivial upper bounds on approximation factors achievable in polynomial time.
U2 - 10.1007/3-540-45071-8_7
DO - 10.1007/3-540-45071-8_7
M3 - Paper in conference proceeding
SN - 978-3-540-40534-4
VL - 2697
SP - 50
EP - 56
BT - Computing and combinatorics / Lecture notes in computer science
PB - Springer
T2 - 9th Annual International Conference, COCOON 2003
Y2 - 25 July 2003 through 28 July 2003
ER -